66 



SOME OF THE PRINCIPLES OP PLANT- BREEDING 



eration hybrids, so that the hybrid plants of the 

 second generation would exhibit these characters 

 in Mendelian proportions, as in the characters 

 described above. The progeny in the second gen- 

 eration would thus exhibit these characters in the 

 following combinations and proportions : IHH to 

 2Hs to Iss. This probable proportion should hold 

 rather constantly, either in small or large numbers 

 of hybrids, though in large numbers it would prob- 

 ably be more accurately realized. The potentiali- 

 ties of the four characters, or two character-pairs, 

 are commingled in the cells of the first-generation 

 hybrid. When the egg-cells or pollen-grains are 

 formed, however, a segregation of the potentiali- 

 ties of the two character-pairs occurs, but inde- 

 pendent of each other. Each egg-cell or pollen- 

 grain will receive only the potentiality of one 

 character of a certain character-pair, but will, at 

 the same time, receive potentialities of other char- 

 acters belonging to other character-pairs. Consid- 

 ering the two character-pairs described, an egg- 

 cell receiving the potentiality of the bald head (B) 

 might contain the potentiality of either H or s, 

 representing the characters of hairy or smooth 

 chaff. These two character-pairs would thus give 

 us egg-cells of four combinations, namely, BH, Bs, 

 bH and bs. 



In the formation of the pollen-grains the same 

 combination occurs, so that with reference to the 

 two character-pairs described, the pollen-grains 

 that would be formed have the same combination 

 of potentialities as the egg-cells, namely, BH, Bs, 

 bH and bs. "We thus have four kinds of egg-cells 

 and four kinds of pollen-grains, so far as these two 

 character-pairs are concerned. If these are brought 

 together, sixteen combinations are possible as 

 follows : 



bsBH 



bsbH 



Examining these combinations carefully, and cut- 

 ting out the letters that occur twice, as the occur- 

 rence of the same potentiality in both egg-cell and 

 and pollen-grain serves only to reproduce the same 

 character, we have the following nine combi- 

 nations, all of which are different: IBH, IBs, IbH, 

 lbs, 2BHs, 2BbH, 2Bbs, 2bHs and 4BbHs. In the 

 illustration taken of the character-pair of bald and 

 bearded heads, and the probable ratio of unions in 

 second-generation hybrids, it was shown that out 

 of 100 unions we should expect, by the law of 

 chance, the ratio 25B to 50Bb to 25b. Now, con- 

 sidering the second character-pair, that is, the 

 hairy and the smooth chaff, in connection with 

 these same 100 unions, we would have the follow- 

 ing as the probable combinations, according to the 

 same law of chance : 



These nine combinations are the same as the 

 nine given above, only multiplied by 6i in each 

 case. In each of the nine combinations when only 

 one of the potentialities of the character is present, 

 the progeny from such an individual from self- 

 fertilized seed will come true to this character in 

 all succeeding generations, as the potentiality of 

 the opposed character has been eliminated. Thus, 

 in the first combination, BH, representing the 

 potentialities of the bald head and hairy chaff, if 

 such a hybrid is fertilized with its own pollen, it 

 will produce only progeny with bald head and 

 hairy chaff. In the second combination, BHs, we 

 have present the potentialities of the bald head of 

 one character-pair and both the hairy and smooth 

 chaff of the other character-pair. Self-fertilized 

 progeny of this hybrid should all come bald, but 

 some should have hairy chaff and some smooth 

 chaff. In the third combination, Bs, we have 

 simply the potentialities of the bald head and 

 smooth chaff, and such a combination should give 

 plants that will come true to type in later genera- 

 tions when self-fertilized. Similar conditions of 

 purity or hybridity of the germ-cells can be figured 

 out for each of the other six combinations. 



If a third character were considered, the propor- 

 tions of the combinations can be determined in 

 exactly the same way. Each one of the above nine 

 possible combinations would be again divided into 

 three different unions in the same way as the 

 three combinations of the one character-pair gave 

 nine different combinations in the second character- 

 pair. In the consideration of the three character- 

 pairs there would thus be 27 different combinations 

 of parental characters. And again in each ovary 

 fecundated, when only one potentiality of each 

 character-pair occurred, the opposing character 

 potentiality befeig in each case eliminated, such a 

 cell should give a plant that would reproduce its 

 characters true to type. It is well known that 

 almost any two different races or species that may 

 be chosen for hybridization will ordinarily differ 

 from each other in numerous characters. When 

 there are a number of these opposing characters 

 which form Mendelian character-pairs, the deter- 

 mination of the possible combinations by Mendel's 

 formulae becomes very complex and diiScult to 

 understand. It is only by taking a few well- 

 marked character -pairs and carefully studying 

 them that the segregation and new combinations 

 according to Mendelian proportions can be followed 

 and understood. Any character - pairs, following 

 Mendel's law, would segregate as indicated above 

 in the case of bald or bearded heads and smooth 

 and hairy chaff of wheat. These characters with 

 wheat have been investigated by Spillman, Hurst 

 and others, and are known to follow very closely 

 Mendelian proportions in their segregation. The 

 same segregation takes place in the case of the 

 bald and bearded barleys, smooth and fuzzy cottons, 

 sweet and starchy kernels in corn, and many other 

 opposed characters in plants. 



It is by no means probable that all characters 

 follow Mendel's law of segregation and recombina- 

 tion, and secondary characters in practical work 



